Bounding the Efficiency Loss of Multi-class Stochastic User Equilibrium under ATIS and Road Tolling
With the dramatical increasement of the motor vehicles,many complex traffic problems have emerged.Information induction and congestion tolling strategy are two common and effective traffic management and control methods,guiding or inducing travelers'route choices to improve system efficiency.Traffic managers often com-bine the Advanced Traveler Information Systems(ATIS)with the congestion tolling strategy,fully utilizing the advantages of both to form an integrated demand management model.As an important part of Intelligent Trans-portation Systems,ATIS enables the sharing and utilization of traffic information,guiding travelers to make cor-rect route choices.Congestion tolling strategy influences travelers'decisions by charging road tolls.Regarding the efficiency loss of the heterogeneous traffic network under ATIS,relevant research only considers the impact of the ATIS penetration rate.However,the influence of the information compliance rate is often ignored on the efficiency loss of ATIS.Scholars have already examined the efficiency loss of road tolling strategy.How the efficiency loss of the traffic network changes under the combined effect of ATIS and tolling strategy is an impor-tant issue for traffic managers.Therefore,it is necessary to theoretically explore the impact of ATIS and tolling strategy on the efficiency of the traffic network.In this paper,based on different heterogeneities,the efficiency loss of heterogeneous traffic network under ATIS and tolling strategy is discussed.Considering that users are heterogeneous in the value of time(VOT)under the road tolling strategy,users have heterogeneity in terms of different information received in a transportation network under ATIS.Based on the two heterogeneities,the efficiency loss of the heterogeneous network is investigated.Firstly,all users are classified into different groups based on the VOT heterogeneity.Then,considering that ATIS essentially depends on the travelers'response to the traffic information,the information compliance rate is introduced.Taking into account the impact of the ATIS penetration rate and the information compliance rate,users are divided into three classes in each group,i.e.,users with ATIS and in compliance with ATIS advice,users with ATIS but not in compliance with ATIS advice,and users without ATIS.Due to the high complexity of heterogeneous traffic net-works under ATIS,travelers only have imperfect information about the network and often choose their travel routes with stochastic uncertainty.Therefore,all users are assumed to follow the stochastic user equilibrium(SUE).Under the assumptions of the logit path choice model,a multi-class SUE model and its equivalent varia-tional inequalities based on the time units and monetary units under ATIS and road tolling strategy are presented.While tolls are considered as part of the total system cost,multi-class system optimum(SO)models under two criteria are constructed.Then the efficiency loss of multi-class SUE against the multi-class SO under both criteria is investigated,and then the upper bounds are presented.Furthermore,for the polynomial travel time function,considering the effect of free flow travel time,the analytic expressions of the tighter upper bound of efficiency loss are derived,and further analysis is made on the parameters influencing the upper bounds,focusing on the influ-ence of the ATIS penetration rate and the information compliance rate on the upper bounds of efficiency loss.The results show that the upper bounds of the efficiency loss decrease with an increase of ATIS penetration rate and the information compliance rate.Besides,the upper bounds are also related to the link cost functions,the users'VOT and familiarity with the network,and the complexity of the network.Finally,the conclusions are validated through a numerical example.The results provide theoretical and technical supports for ATIS and road tolling strategy design,and then achieves optimal control of traffic system.The next step will extend our research from a deterministic network to a stochastic network,aiming to investigate the efficiency loss of multi-class equi-librium in a stochastic heterogeneous network.
ATISroad tollingmulti-class stochastic user equilibriummulti-class system optimumefficiency loss
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